How do you do an island select?
As you have joined the two objects, they are now one object. In order to edit/select the geometry of an object, you must be in edit mode.

You can press &#8633; Tab to toggle edit mode, or set the mode via the selector in 3D view > header:



Once in edit mode, L works as expected:



Note that you can also select geometry connected the selected geometry with &#9096; CtrlL: